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Least Common Multiple of 12 and 30

Free LCM Calculator determines the least common multiple (LCM) between 12 and 30 the smallest integer that is 60 that is divisible by both numbers.

Least Common Multiple (LCM) of 12 and 30 is 60.

LCM(12,30) = 60

LCM of 12 and 30

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple (LCM) of 30 and 12 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 12. First we will calculate the prime factors of 30 and 12.

Prime Factorization of 30


2 30
3 15
5 5
1

Prime factors of 30 are 2, 3,5. Prime factorization of 30 in exponential form is:

30 = 21×31×51

Prime Factorization of 12


2 12
2 6
3 3
1

Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:

12 = 22×31

Now multiplying the highest exponent prime factors to calculate the LCM of 30 and 12.

LCM(30,12) = 22×31×51
LCM(30,12) = 60

Factors of 30

List of positive integer factors of 30 that divides 30 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1, 2, 3, 4, 6, 12

Least Common Multiple of 30 and 12 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30 and 12, than apply into the LCM equation.

GCF(30,12) = 6
LCM(30,12) = ( 30 × 12) / 6
LCM(30,12) = 360 / 6
LCM(30,12) = 60

Least Common Multiple of 30 and 12 by Listing Multiples

Multiples of 30

30,60

Multiples of 12

12, 24, 36, 48,60

Find the smallest number that is on all of the lists. We have it in bold above.

∴ Least Common Multiple of 30 and 12 is 60

Properties of LCM 30 and 12

(i) The LCM of 12 and 30 is associative

LCM of 30 and 12 = LCM of 12 and 30

Frequently Asked Questions on LCM of 30 and 12

1. What is the LCM of 30 and 12?

Answer: LCM of 30 and 12 is 60.

2. What are the Factors of 30?

Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.

3. What are the Factors of 12?

Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.

4. How to Find the LCM of 30 and 12?

Answer:

Least Common Multiple of 30 and 12 = 60

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

Step 2: Find the prime factorization of 12

12 = 2 x 2 x 3

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 60 = 2 x 2 x 3 x 5

Step 4: Therefore, the least common multiple of 30 and 12 is 60.